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math.AT2025
Persistent Homology for Labeled Datasets: Gromov-Hausdorff Stability and Generalized Landscapes
Yaoying Fu, Evgeniya Lagoda, Shiying Li +3
Techniques from metric geometry have become fundamental tools in modern mathematical data science, providing principled methods for comparing datasets modeled as finite metric spac…
stat.ML2025
Metrics for Parametric Families of Networks
Mario Gómez, Guanqun Ma, Tom Needham +1
We introduce a general framework for analyzing data modeled as parameterized families of networks. Building on a Gromov-Wasserstein variant of optimal transport, we define a family…
stat.ML2025
Conic Formulations of Transport Metrics for Unbalanced Measure Networks and Hypernetworks
Mary Chriselda Antony Oliver, Emmanuel Hartman, Tom Needham
The Gromov-Wasserstein (GW) variant of optimal transport, designed to compare probability densities defined over distinct metric spaces, has emerged as an important tool for the an…